Plane and Spherical TrigonometryD.C. Heath & Company, 1917 - 313 páginas |
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Página 1
... represent the same segment measured in opposite direc- tions ; hence AC = CA or AC = CA. - - Also , if B be a third point on the line , the segments AB and BA are opposite in sign ; likewise the segments BC and CB . and Hence AB = - BA ...
... represent the same segment measured in opposite direc- tions ; hence AC = CA or AC = CA. - - Also , if B be a third point on the line , the segments AB and BA are opposite in sign ; likewise the segments BC and CB . and Hence AB = - BA ...
Página 8
... central angle subtended by the given arc , hence 8 Α r = angle AOB arc AB radius = the length of the arc AB by a , the where angle AOB is expressed in radians . Representing 8 TRIGONOMETRY Relation between angle, radius, and arc.
... central angle subtended by the given arc , hence 8 Α r = angle AOB arc AB radius = the length of the arc AB by a , the where angle AOB is expressed in radians . Representing 8 TRIGONOMETRY Relation between angle, radius, and arc.
Página 9
... represented by v . During the same time t , the angle is generated ; and 0 / t is called the angular velocity , and is represented by the Greek letter w ( omega ) . W Dividing Equation ( 1 ) , Art . 17 , RECTANGULAR COORDINATES AND ...
... represented by v . During the same time t , the angle is generated ; and 0 / t is called the angular velocity , and is represented by the Greek letter w ( omega ) . W Dividing Equation ( 1 ) , Art . 17 , RECTANGULAR COORDINATES AND ...
Página 53
... standpoint of ratios ; but each function can also be represented in magnitude and sign by a single line . Let LOP be any angle . Take OP = 1 FUNDAMENTAL RELATIONS 53 LINE VALUES Representation of the trigonometric functions by lines.
... standpoint of ratios ; but each function can also be represented in magnitude and sign by a single line . Let LOP be any angle . Take OP = 1 FUNDAMENTAL RELATIONS 53 LINE VALUES Representation of the trigonometric functions by lines.
Página 55
... represent the trigonometric functions in sign as well as in magnitude . The segments which represent the trigonometric functions are called the line values of the functions . PROBLEM . Represent vers a and covers a by line values . 58 ...
... represent the trigonometric functions in sign as well as in magnitude . The segments which represent the trigonometric functions are called the line values of the functions . PROBLEM . Represent vers a and covers a by line values . 58 ...
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Términos y frases comunes
angle opposite angles of depression colog COMMON LOGARITHMS complex number computed cos a cos cos-¹ cos¹ cos² cos³ cot-¹ cot² cotangent coty csc² cube root decimal point determine difference Equating the real Find the height find the value flagpole four-place tables fundamental relations given angles greater than 90 Hence interpolation inverse function law of cosines law of sines law of tangents less than 180 line values Log Cot log sin ẞ loga logarithms of numbers mantissa Moivre's theorem negative number of degrees quadrant radians roots of unity sec-¹ sec² sides are given Similarly sin a cos sin a sin sin-¹ sin(a+b sin¹ sin² sin³ solution Solve the following spherical right triangle spherical triangle square root ẞ cot tan-¹ tan² tangent terminal line tower trigonometric functions Va² α α απ π π ייד
Pasajes populares
Página 4 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 130 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 4 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 111 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Página 3 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Página 85 - B is negative, and BD — — a cos B. The substitution of this in (4) leads us again to (3). Thus we see that (3) is true in all cases. THE LAW OF COSINES. The square of any side .of a plane triangle is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle. This may be regarded as a generalization of the Pythagorean Theorem to which it reduces when the included angle is a right angle. These two laws are among the most important of...
Página 2 - If the number is greater than 1, the characteristic is one less than the number of places to the left of the decimal point.
Página 131 - By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b...
Página 31 - The product of all the lines, that can be drawn from one of the angles of a regular polygon of n sides, inscribed in a circle whose radius is a, to all the other angular points = no.
Página 111 - From the top of a cliff 150 ft. high the angles of depression of the top and bottom of a tower are 30° and 60°, respectively.